The generator matrix
1 1 1 X 1 1 1 1
0 X 2X X 0 0 0 0
0 0 6 0 0 0 6 0
0 0 0 3 0 0 6 0
0 0 0 0 6 0 6 0
0 0 0 0 0 6 3 0
generates a code of length 8 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+48x^6+160x^9+372x^12+2916x^14+540x^15+8748x^16+5832x^17+604x^18+420x^21+42x^24
The gray image is a code over GF(3) with n=72, k=9 and d=18.
This code was found by Heurico 1.16 in 0.0374 seconds.